Question

MOD . Please Help

Answer 1

\[\huge \left| x \right|^{2} - \left| x \right| +1 =0 \]
The number of real roots of this are

Answer 2

@mathslover

Answer 3

@BSwan @jim_thompson5910 @Miracrown

Answer 4

No solutions

Answer 5

Answer is 4 sollutions

Answer 6

I know imaginary roots come from both cases

Answer 7

Not from the second case

Answer 8

\[|x|^2-|x|+1=0 \implies -|x|=-1-|x|^2 \implies |x|=1+|x|^2\]

\[x = 1+|x|^2 ~ ~ or ~ ~x=-1-|x|^2\]

\[-x^2+x-1=0 ~~~~ or ~~~~ x=-1-|x|^2\]

You can factor etc, which will lead to no solutions.

Answer 9

Put, |x| = y, then, you get,

\[y^2 - y + 1 = 0\]
\[\implies y = \cfrac{1 \pm \sqrt{1 - 4}}{2}\]

This gives no real root.

So, the given equation will not have any real root as @iambatman said.

Answer 10

\[\begin{align*}
|x|^2-|x|+1&=0\\
|x|^2-|x|+\frac{1}{4}+\frac{3}{4}&=0\\\\\\
\left(|x|-\frac{1}{2}\right)^2+\frac{3}{4}&=0\\\\\\
\left(|x|-\frac{1}{2}\right)^2&=-\frac{3}{4}
\end{align*}\]
To reiterate what everyone else is saying: no real roots.

Answer 11

Yes got the same thing you all did lol , the answer in the textbook was incorrect